1. Field of the Invention
The present invention relates to a method for measuring distance and areas by mobile devices combined with light beam projectors, especially to one that can conveniently calculate the distance between two points and that can further calculate the measure of areas, achieving a convenient and augmented effectiveness in the measuring process.
2. Description of the Related Art
FIGS. 1˜4 illustrated a distance measurement system and method disclosed in Taiwan Publication No. I289196. It calculates the actual distance between the target object and the image capturing device based on the proportional relationship of the pixel values and the actual length of distance from the target object. FIG. 1 is a functional block diagram thereof. There is a laser light source 20 projecting a laser beam on the surface of the target object 30 and a digital camera 10 retrieving image information, then a computing unit 40 calculating the pixel values of the image so as to detects the actual length of the target object 30 or the distance between which and the digital camera 10 with the proportional relationship between the pixel values and the distance from the target object 30.
FIG. 2 is a schematic diagram illustrating the distance measuring by the pixel values according to the system and method. The digital camera 10 individually retrieves image information on the line CD and EF with the laser source 20 individually projecting a point thereon, where
OP denotes the optical point of origin of the digital camera 10;
PD and PF denote the projected points on the plane CD and EF respectively projected by the laser light source 20;
O denotes the center of the scanned plane captured by the digital camera 10;
HD denotes the distance between the plane CD and the digital camera 10;
HF denotes the distance between the plane EF and the digital camera 10;
hS denotes the distance between the point OP and the digital camera 10;
DD and DF denote the maximal values of the length that can be captured on the plane CD and EF respectively by the digital camera 10;
Dr denotes the distance between PD, PF and O:
2θmax denotes the maximal angle for the digital camera 10 to capture;
Nmax denotes the maximal pixel values of a single scanning line of the digital camera 10; and
ND and NF denote the pixel values of the distance between PD, PF and O respectively.
Referring to the projected perspective view of an image retrieved by the digital camera 10 as shown in FIG. 3, the axle Z is the direction of image retrieving of the optical point of origin OP along which the digital camera 10 retrieves the image and the image information of scanned plane including a point A and point B. The direction of the axle Z is also the direction of the normal line of the scanned plane, and the point on the scanned plane passed through by the axle Z is the center of the plane O. The line between point C and D and the line between point E and F are the scanned lines crossed by the point O and a scanned plane; each crossing point on the lines is right at the position of the
      1    2    ⁢      N          ma      ⁢                          ⁢      x      pixel point.
Referring to FIG. 2 again, the laser beam projected by the laser light source 20 is parallel to the direction of the image retrieved by the digital camera 10, resulting in the laser beam being perpendicular to any plane scanned by the digital camera 10 and resulting in the projected points PD, PF projected by the laser beam on the scanned planes having the same length of distance Dr between each point and the point O on the planes.
With the feature of having the same length of distance Dr between each projected points PD, PF and the point O on the planes, it is able to obtain a horizontal distance Dr by a single laser light source projecting on any plane instead of two laser light sources. In addition, the time for scanning the image information captured by the digital camera 10 and the actual distance between the digital camera 10 and the target object have a linear proportion relation, thus the computing unit 40 can present the distance with the pixel values in the following formulas:
            D      D        =                                        N                          ma              ⁢                                                          ⁢              x                                            N            D                          ×                  D          r                ⁢                                  ⁢        and        ⁢                                  ⁢                  D          F                    =                                    N                          ma              ⁢                                                          ⁢              x                                            N            F                          ×                  D          r                      ;
On the other hand, the following formulas come from the Triangle Theorem:
            H      D        =                                        1            2                    ⁢                      D            D                    ⁢          cot          ⁢                                          ⁢                      θ                          ma              ⁢                                                          ⁢              x                                      -                              h            s                    ⁢                                          ⁢          and          ⁢                                          ⁢                      H            F                              =                                    1            2                    ⁢                      D            F                    ⁢          cot          ⁢                                          ⁢                      θ                          ma              ⁢                                                          ⁢              x                                      -                  h          s                      ;
Then we can infer the following formulas from the one above:
            H      D        =                            1          2                ⁢                  (                                                                      N                  s                                ⁡                                  (                  max                  )                                                            N                D                                      ×                          D              r                                )                ⁢        cot        ⁢                                  ⁢                  θ                      ma            ⁢                                                  ⁢            x                              -                        h          s                ⁢                                  ⁢        and                        H      F        =                            1          2                ⁢                  (                                                                      N                  s                                ⁡                                  (                  max                  )                                                            N                F                                      ×                          D              r                                )                ⁢        cot        ⁢                                  ⁢                  θ                      ma            ⁢                                                  ⁢            x                              -                        h          s                .            
The cot θmax and hs in the inferred formulas can be calculated in advance by a calculation model, and then the computing unit 40 is able to find the values of ND and NF, and further the ones of HD and HF with the formulas.
In FIG. 4, a structure diagram of a calculation model for calculating parameter values according to the prior art, the calculation model includes the digital camera 10, two vertical rulers 41, and two horizontal rulers 43; the perpendicular distance hm1, hm2 between each horizontal rulers 43 and the surface of the digital camera 10 can be measured by the vertical rulers 41. The maximal angle 2θmax to be captured by the digital camera 10 is restricted to 2θs for the accuracy of the measurement of hs in the calculation model; in this way, the edges of the scanned plane would be eliminated in case of blur edges.
Furthermore, when the maximal angle is restricted to 2θs, the maximal horizontal distances Dm1, Dm2 for the digital camera 10 to capture can also be easily measured and calculated by the Triangle Theorem with the following formulas:
            h      s        +          h              m        ⁢                                  ⁢        1              =                              1          2                ⁢                  D                      m            ⁢                                                  ⁢            1                          ⁢        cot        ⁢                                  ⁢                  θ          s                ⁢                                  ⁢        and        ⁢                                  ⁢                  h          s                    +              h                  m          ⁢                                          ⁢          2                      =                  1        2            ⁢              D                              m            ⁢                                                  ⁢            2                    ⁢                                                    ⁢      cot      ⁢                          ⁢                        θ          s                .            
Then we can infer the formula for the value of cot θs as following.
                    h                  m          ⁢                                          ⁢          1                    -              h                  m          ⁢                                          ⁢          2                      =                  1        2            ⁢              (                              D                          m              ⁢                                                          ⁢              1                                -                      D                          m              ⁢                                                          ⁢              2                                      )            ⁢      cot      ⁢                          ⁢              θ        s                        cot      ⁢                          ⁢              θ        s              =          2      ⁢                          ⁢                                    h                          m              ⁢                                                          ⁢              2                                -                      h                          m              ⁢                                                          ⁢              1                                                            D                          m              ⁢                                                          ⁢              2                                -                      D                          m              ⁢                                                          ⁢              1                                          
Then we can further infer the following proportion relation by comparing the formulas above with angle θs and 2θmax.
                    h        s            +              h                  m          ⁢                                          ⁢          2                                    h        s            +              h                  m          ⁢                                          ⁢          1                      =            D              m        ⁢                                  ⁢        2                    D              m        ⁢                                  ⁢        1            
Therefore the value of hs can be found in the following inferred formula.
      h    s    =                              h                      m            ⁢                                                  ⁢            1                          ⁢                  D                      m            ⁢                                                  ⁢            2                              -                        h                      m            ⁢                                                  ⁢            2                          ⁢                  D                      m            ⁢                                                  ⁢            1                                              D                  m          ⁢                                          ⁢          1                    -              D                  m          ⁢                                          ⁢          2                    
Another measurement tool is a laser rangefinder which emits laser beam to the target object and calculates the distance in-between by receiving the laser signals reflected to a laser signal receiver, usually an Avalanche Photo Diode (APD), that turns the laser signals into electric signals. The equation of the calculation is
  Td  =      2    ⁢                  ⁢          L      C      where Td denotes the delayed period between sending and receiving the signals; L denotes the distance between the origin of measurement and the target object; C denotes the velocity of light transmission. Therefore, measuring the delayed period Td leads to the distance L by calculation.
As technologies getting advanced, laser rangefinders are widely applied in construction engineering, decoration engineering, etc. As shown in FIG. 5, a laser rangefinder 100 is used to measure the table 101. If the table 101 is placed along the wall, the signals would reflect by the wall and then we can find the length of distance L.
However, there is still room for improvements. Firstly, the measurer should be at a fixed position to project the laser beam to the pre-determined measuring point instead of any measuring point in the space, making the measurement inconvenient. Secondly, since the laser beam is projected to the pre-determined measuring point, it can only calculate the distance but not the measure of the area surrounded by any measuring point and the point of the origin.